Multi-window Gabor Frames in Amalgam Spaces
نویسندگان
چکیده
We show that multi-window Gabor frames with windows in the Wiener algebra W (L∞, `) are Banach frames for all Wiener amalgam spaces. As a by-product of our results we prove the canonical dual of a Gabor frame with a continuous generator in the Wiener algebra also belongs to this space. Our proofs are mostly based on recent noncommutative versions of Wiener’s 1/f lemma.
منابع مشابه
Projective Modules over Noncommutative Tori Are Multi-window Gabor Frames for Modulation Spaces
In the present investigation we link noncommutative geometry over noncommutative tori with Gabor analysis, where the first has its roots in operator algebras and the second in time-frequency analysis. We are therefore in the position to invoke modern methods of operator algebras, e.g. topological stable rank of Banach algebras, to exploit the deeper properties of Gabor frames. Furthermore, we a...
متن کاملGabor Analysis in Weighted Amalgam Spaces
Gabor frames {e2πinβ·xg(x− kα)}n,k∈Zd provide series representations not only of functions in L(R) but of the entire range of spaces M ν known as the modulation spaces. Membership of a function or distribution f in the modulation space is characterized by a sequence-space norm of the Gabor coefficients of f depending only on the magnitudes of those coefficients, and the Gabor series representat...
متن کاملWiener Amalgam Spaces for the Fundamental Identity of Gabor Analysis
In the last decade it has become clear that one of the central themes within Gabor analysis (with respect to general timefrequency lattices) is a duality theory for Gabor frames, including the Wexler-Raz biorthogonality condition, the Ron-Shen’s duality principle or Janssen’s representation of a Gabor frame operator. All these results are closely connected with the so-called Fundamental Identit...
متن کاملDigital Gabor Filters with Mra Structure*
Digital Gabor filters are indispensable tools of local time-frequency analysis in signal processing. With strong orientation selectivity, discrete (tight) Gabor frames generated by 2D Gabor filters also see their wide applications in image processing and volume data processing. However, owing to the lack of multi-scale structures, discrete Gabor frames are less effective than multiresolution an...
متن کاملConstructive realization of dual systems for generators of multi-window spline-type spaces
Multi-window spline-type spaces arise naturally in many areas. Among others they have been used as model spaces in the theory of irregular sampling. This class of shift-invariant spaces is characterized by possessing a Riesz basis which consists of a set of translates along some lattice Λ of a finite family of atoms. Part of their usefulness relies on the explicit knowledge of the structure of ...
متن کامل